Path: ...!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail
From: "B. Pym" <No_spamming@noWhere_7073.org>
Newsgroups: comp.lang.scheme
Subject: Euler 14.
Date: Tue, 28 May 2024 11:33:16 -0000 (UTC)
Organization: A noiseless patient Spider
Lines: 38
Message-ID: <v34fdq$it4b$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=iso-8859-1
Injection-Date: Tue, 28 May 2024 13:33:16 +0200 (CEST)
Injection-Info: dont-email.me; posting-host="45ccecf5734ae6486bc629ee94fff335";
	logging-data="619659"; mail-complaints-to="abuse@eternal-september.org";	posting-account="U2FsdGVkX19Vaz6iPu1ZzPNnLPDGXkeT"
User-Agent: XanaNews/1.18.1.6
Cancel-Lock: sha1:Jt9la7wzm3eyOcXo3H8LsmpuACI=
Bytes: 1680

The following iterative sequence is defined for the set of positive
integers:

	  n -> n/2 (n is even)
	  n -> 3n + 1 (n is odd)

Using the rule above and starting with 13, we generate the following
sequence:

	  13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1

It can be seen that this sequence (starting at 13 and
finishing at 1) contains 	10 terms. Although it has not been
proved yet (Collatz Problem), it is thought 	that all starting
numbers finish at 1.

Which starting number, under one million, produces the longest chain?

NOTE: Once the chain starts the terms are allowed to go above one
million.


Gauche Scheme

(use gauche.collection) ;; find-max


(define (cltz n) (if (odd? n) (+ 1 (* n 3)) (/ n 2)))

(define (d c n)
  (if (= n 1) c (d (+ 1 c) (cltz n))))

(find-max (lrange 1 1000000) :key (pa$ d 1))

  ===>
837799